Minimization of the maximum peak-to-peak gain: the general multiblock problem

A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented. By formulating the interpolation conditions in a concise and natural way, the general theory is developed in simpler terms and with a mi...

Full description

Saved in:

Bibliographic Details
Published in:	IEEE transactions on automatic control Vol. 38; no. 10; pp. 1459 - 1482
Main Authors:	Diaz-Bobillo, I.J., Dahleh, M.A.
Format:	Journal Article
Language:	English
Published:	New York, NY IEEE 01.10.1993 Institute of Electrical and Electronics Engineers
Subjects:	Applied sciences Computer science; control theory; systems Control systems Control theory. Systems Delay Design optimization Exact sciences and technology Interpolation Iterative methods Linear programming Optimal control Polynomials Robustness Time domain analysis Vectors Interpolation Suboptimal control Optimal solution Control synthesis Linear programming Aircraft Optimization
ISSN:	0018-9286
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented. By formulating the interpolation conditions in a concise and natural way, the general theory is developed in simpler terms and with a minimum number of assumptions. In addition, further insight is gained into the structure of the optimal solution, and different classes of multiblock problems are distinguished. This leads to a conceptually attractive, iterative method for finding approximate solutions.< >
AbstractList	A comprehensive study of the general < e1 > l < /e1 > (1)-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented. By formulating the interpolation conditions in a concise and natural way, the general theory is developed in simpler terms and with a minimum number of assumptions. In addition, further insight is gained into the structure of the optimal solution, and different classes of multiblock problems are distinguished. This leads to a conceptually attractive, iterative method for finding approximate solutions A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented. By formulating the interpolation conditions in a concise and natural way, the general theory is developed in simpler terms and with a minimum number of assumptions. In addition, further insight is gained into the structure of the optimal solution, and different classes of multiblock problems are distinguished. This leads to a conceptually attractive, iterative method for finding approximate solutions.< >
Author	Dahleh, M.A. Diaz-Bobillo, I.J.
Author_xml	– sequence: 1 givenname: I.J. surname: Diaz-Bobillo fullname: Diaz-Bobillo, I.J. organization: Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA – sequence: 2 givenname: M.A. surname: Dahleh fullname: Dahleh, M.A. organization: Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3799630$$DView record in Pascal Francis
BookMark	eNqNkDtPw0AQhK8IEklAoqZygRCNw738ODoU8ZIS0UB9Wl_W4cj5HHyOBPx6nDhQIAqq0Wq-mZVmRAa-9kjICaMTxqi6VBMuWZKyARlSyvJY8Tw9JKMQXrszlZINyXxuva3sJ7S29lFdRu0LRhW822pTRWuEVdzW8VajJVh_tbOX6LEBF1Ub19rC1WYVrZu6cFgdkYMSXMDjvY7J8-3N0_Q-nj3ePUyvZ7GRImljgwJBpYYaWYgkSYEyWTKGkhtYUIbcKFoow3MuYSFlKdPcKJmUKFTBOYAYk_O-t_v7tsHQ6soGg86Bx3oTNM9VxrOM_QMUiaKZ6MCzPQjBgCsb8MYGvW5sBc2HFplSqaAdNukx09QhNFhqY9vddm0D1mlG9XZ5rXS_fBe4-BX4rvwDPe1Ri4g_2N78ApPGjos
CODEN	IETAA9
CitedBy_id	crossref_primary_10_1109_ACCESS_2022_3222487 crossref_primary_10_1002_rnc_5932 crossref_primary_10_1109_9_536517 crossref_primary_10_1016_j_amc_2008_05_119 crossref_primary_10_1109_9_481518 crossref_primary_10_1109_9_536510 crossref_primary_10_1016_j_cnsns_2011_11_033 crossref_primary_10_1080_0020717031000115967 crossref_primary_10_1177_0142331213492367 crossref_primary_10_1016_j_sigpro_2009_07_018 crossref_primary_10_1109_TAC_2003_819072 crossref_primary_10_1109_9_277236 crossref_primary_10_1016_S0005_1098_99_00184_3 crossref_primary_10_1109_9_471209 crossref_primary_10_1109_9_847104 crossref_primary_10_1109_9_633826 crossref_primary_10_1631_jzus_2005_A0707 crossref_primary_10_1109_ACCESS_2020_2996211 crossref_primary_10_1016_0005_1098_94_00123_Z crossref_primary_10_1016_S0005_1098_96_00126_4 crossref_primary_10_1093_imamci_dnaa017 crossref_primary_10_1080_00207721_2018_1482381 crossref_primary_10_1002_aic_690411110 crossref_primary_10_2514_2_4613 crossref_primary_10_1109_TAC_2000_880990 crossref_primary_10_1016_S0167_6911_02_00174_3 crossref_primary_10_1002_rnc_70165 crossref_primary_10_1007_s12555_018_0173_z crossref_primary_10_1002_rnc_5513 crossref_primary_10_1109_TAC_2015_2452815 crossref_primary_10_1016_j_neucom_2015_02_025 crossref_primary_10_1109_9_489274 crossref_primary_10_2514_2_4305 crossref_primary_10_1023_A_1022641516007 crossref_primary_10_1109_9_489218 crossref_primary_10_1109_TAC_2003_809143 crossref_primary_10_1080_00207179_2017_1288301 crossref_primary_10_1109_TAC_2015_2417838 crossref_primary_10_1049_ip_cta_20030141 crossref_primary_10_1109_9_839942 crossref_primary_10_1109_TSMC_2018_2855190 crossref_primary_10_1109_9_376108 crossref_primary_10_1002_acs_2938 crossref_primary_10_1109_9_718608 crossref_primary_10_1007_s00034_012_9462_6 crossref_primary_10_1109_9_718607 crossref_primary_10_1002_rnc_6685 crossref_primary_10_1524_auto_2006_54_9_437 crossref_primary_10_1109_9_580863
Cites_doi	10.1109/TAC.1987.1104455 10.1016/0167-6911(88)90070-9 10.1109/9.119635 10.1109/9.1288 10.1109/TCS.1974.1083805 10.1109/TAC.1986.1104315 10.1080/00207177608932805 10.1109/9.58544 10.1016/0005-1098(91)90080-L 10.1080/00207178908953438 10.1109/9.85063 10.1109/9.126577 10.1109/9.109641 10.1109/TCS.1979.1084628 10.1016/0005-1098(82)90070-X 10.1109/9.75099 10.1109/9.277236 10.1109/CDC.1990.203729 10.1007/BF00940510 10.1109/TAC.1976.1101223 10.1109/TAC.1987.1104603 10.1109/9.7246 10.1016/0005-1098(93)90173-Q 10.1007/978-3-0348-5469-6_1 10.1016/0167-6911(87)90002-8 10.1016/0167-6911(89)90084-4 10.1016/0167-6911(92)90092-7 10.1109/9.53547 10.1007/978-3-0348-7701-5_3
ContentType	Journal Article
Copyright	1994 INIST-CNRS
Copyright_xml	– notice: 1994 INIST-CNRS
DBID	AAYXX CITATION IQODW 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D H8D
DOI	10.1109/9.241561
DatabaseName	CrossRef Pascal-Francis Computer and Information Systems Abstracts Electronics & Communications Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Aerospace Database
DatabaseTitle	CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional Aerospace Database
DatabaseTitleList	Technology Research Database Technology Research Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Applied Sciences
EndPage	1482
ExternalDocumentID	3799630 10_1109_9_241561 241561
GroupedDBID	-~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACGFS ACIWK ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P RIA RIE RNS TAE TN5 VH1 VJK ~02 AAYXX CITATION AAYOK IQODW RIG 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D H8D
ID	FETCH-LOGICAL-c435t-ce3ea96c0c4b3556a014f11e42cad01e2c90b9c2824ad44f468c945fe39b22aa3
IEDL.DBID	RIE
ISICitedReferencesCount	67
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=10_1109_9_241561&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0018-9286
IngestDate	Sat Sep 27 20:32:31 EDT 2025 Mon Sep 29 05:25:01 EDT 2025 Wed Apr 02 07:26:17 EDT 2025 Sat Nov 29 02:20:21 EST 2025 Tue Nov 18 22:35:44 EST 2025 Wed Aug 27 02:51:59 EDT 2025
IsDoiOpenAccess	false
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	10
Keywords	Interpolation Suboptimal control Optimal solution Control synthesis Linear programming Aircraft Optimization
Language	English
License	https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c435t-ce3ea96c0c4b3556a014f11e42cad01e2c90b9c2824ad44f468c945fe39b22aa3
Notes	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
OpenAccessLink	http://hdl.handle.net/1721.1/3260
PQID	28359073
PQPubID	23500
PageCount	24
ParticipantIDs	proquest_miscellaneous_28972771 pascalfrancis_primary_3799630 crossref_citationtrail_10_1109_9_241561 crossref_primary_10_1109_9_241561 ieee_primary_241561 proquest_miscellaneous_28359073
PublicationCentury	1900
PublicationDate	1993-10-01
PublicationDateYYYYMMDD	1993-10-01
PublicationDate_xml	– month: 10 year: 1993 text: 1993-10-01 day: 01
PublicationDecade	1990
PublicationPlace	New York, NY
PublicationPlace_xml	– name: New York, NY
PublicationTitle	IEEE transactions on automatic control
PublicationTitleAbbrev	TAC
PublicationYear	1993
Publisher	IEEE Institute of Electrical and Electronics Engineers
Publisher_xml	– name: IEEE – name: Institute of Electrical and Electronics Engineers
References	ref13 ref12 ref37 ref15 ref36 ref14 ref31 ref30 ref33 ref11 ref32 ref10 kreyszig (ref25) 1989 ref2 ref1 ref17 ref38 ref16 luenberger (ref27) 1984 ref19 gohberg (ref21) 1982 golub (ref22) 1983 kailath (ref23) 1980 ref24 ref20 luenberger (ref26) 1969 stein (ref35) 1987 ref28 ref29 ref8 ref7 ref9 ref4 ref3 diaz-bobillo (ref18) 1992 ref6 ref5 staffans (ref34) 1990
References_xml	– ident: ref10 doi: 10.1109/TAC.1987.1104455 – ident: ref13 doi: 10.1016/0167-6911(88)90070-9 – ident: ref6 doi: 10.1109/9.119635 – ident: ref11 doi: 10.1109/9.1288 – ident: ref16 doi: 10.1109/TCS.1974.1083805 – ident: ref37 doi: 10.1109/TAC.1986.1104315 – ident: ref28 doi: 10.1080/00207177608932805 – ident: ref15 doi: 10.1109/9.58544 – ident: ref29 doi: 10.1016/0005-1098(91)90080-L – year: 1980 ident: ref23 publication-title: Linear Systems – ident: ref31 doi: 10.1080/00207178908953438 – ident: ref32 doi: 10.1109/9.85063 – ident: ref19 doi: 10.1109/9.126577 – year: 1983 ident: ref22 publication-title: Matrix Computations – year: 1969 ident: ref26 publication-title: Optimization by vector space methods – ident: ref14 doi: 10.1109/9.109641 – ident: ref36 doi: 10.1109/TCS.1979.1084628 – ident: ref20 doi: 10.1016/0005-1098(82)90070-X – ident: ref24 doi: 10.1109/9.75099 – year: 1990 ident: ref34 publication-title: On the Four-block Model Matching Problem in l – year: 1989 ident: ref25 publication-title: Introductory Functional Analysis With Applications – ident: ref3 doi: 10.1109/9.277236 – ident: ref4 doi: 10.1109/CDC.1990.203729 – ident: ref33 doi: 10.1007/BF00940510 – ident: ref38 doi: 10.1109/TAC.1976.1101223 – year: 1992 ident: ref18 publication-title: The general II Optimal Problem Exact and Approximate Solutions – year: 1982 ident: ref21 publication-title: Matrix Polynomials – ident: ref9 doi: 10.1109/TAC.1987.1104603 – year: 1987 ident: ref35 article-title: H? Workshop, Session II publication-title: Proc IEEE Conf Decision Contr – ident: ref12 doi: 10.1109/9.7246 – ident: ref8 doi: 10.1016/0005-1098(93)90173-Q – ident: ref1 doi: 10.1007/978-3-0348-5469-6_1 – ident: ref5 doi: 10.1016/0167-6911(87)90002-8 – ident: ref30 doi: 10.1016/0167-6911(89)90084-4 – ident: ref17 doi: 10.1016/0167-6911(92)90092-7 – ident: ref7 doi: 10.1109/9.53547 – year: 1984 ident: ref27 publication-title: Linear and Nonlinear Programming – ident: ref2 doi: 10.1007/978-3-0348-7701-5_3
SSID	ssj0016441
Score	1.7064812
Snippet	A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are... A comprehensive study of the general < e1 > l < /e1 > (1)-optimal multiblock problem and a new linear programming algorithm for computing suboptimal...
SourceID	proquest pascalfrancis crossref ieee
SourceType	Aggregation Database Index Database Enrichment Source Publisher
StartPage	1459
SubjectTerms	Applied sciences Computer science; control theory; systems Control systems Control theory. Systems Delay Design optimization Exact sciences and technology Interpolation Iterative methods Linear programming Optimal control Polynomials Robustness Time domain analysis Vectors
Title	Minimization of the maximum peak-to-peak gain: the general multiblock problem
URI	https://ieeexplore.ieee.org/document/241561 https://www.proquest.com/docview/28359073 https://www.proquest.com/docview/28972771
Volume	38
WOSCitedRecordID	wos10_1109_9_241561&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) issn: 0018-9286 databaseCode: RIE dateStart: 19630101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://ieeexplore.ieee.org/ omitProxy: false ssIdentifier: ssj0016441 providerName: IEEE
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8QwEA4qHvTgY1VcdTWC4KmaJukj3kQUD7p4UPBW0ulkKbrdxd2KP98k7S6KInhq6UxpmWky3zSTbwg5iYUwUnEMgEc8kGECQSpzGVh0UJgo0iY3vmvJXdLvp8_P6qHl2fZ7YRDRF5_hmTv1a_nFCGr3q-zcZxs21VlMkrjZqjVfMHBhvZl07fjladzyzIZMnauz5r5vkce3UnGFkHpibWGaJhY_5mMfZG7W__V6G2StxZL0snH-JlnAqkNWvzAMbpH7-7Iqh-1eSzoy1OI9OtQf5bAe0jFqx9wfuCMd6LK68OJBw0RNfa1hboPdC23bzmyTp5vrx6vboO2gEICFQdMAUKBWMTCQuQUWsbYJkQlDlBx0wULkoFiuwKZdUhdSGhmnoGRkUKicc63FDlmqRhXuEqrASgALYMaRDIJmsogYxoXgIrcgsktOZ9bNoKUXd10uXjOfZjCVqawxUJcczzXHDaXGLzodZ9-5fHa1981fc7FIbNomWJcczfyX2VHilj50haN6kjlWOWVns780lIVySbj365P3yYqvdPRVfAdkafpWY48sw_u0nLwd-k_xExev3nY
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3dS8MwEA-igvrgx1ScnxEEn6ppknaLbyKK4jZ8UNhbSa-XUXTd2If455uk3VAUwaeW3pWWuyb3u-byO0LOYiGMVBwD4BEPZNiAoClTGVh0kJko0iY1vmtJq9HpNLtd9VTxbPu9MIjoi8_wwp36tfxsAFP3q-zSZxs21VmKpOSs3Kw1XzJwgb2cdu0I5s24YpoNmbpUF-Wd32KPb6biSiH12FrDlG0sfszIPszcbfzrBTfJeoUm6XXp_i2ygEWNrH3hGNwm7XZe5P1qtyUdGGoRH-3rj7w_7dMhasfdH7gj7em8uPLiXslFTX21YWrD3SutGs_skJe72-eb-6DqoRCABUKTAFCgVjEwkKmFFrG2KZEJQ5QcdMZC5KBYqsAmXlJnUhoZN0HJyKBQKedai12yWAwK3CNUgZUAZsCMoxkEzWQWMYwzwUVqYWSdnM-sm0BFMO76XLwlPtFgKlFJaaA6OZ1rDktSjV90as6-c_ns6tE3f83FomETN8Hq5GTmv8SOE7f4oQscTMeJ45VTdj77S0NZMNcI93998glZuX9ut5LWQ-fxgKz6ukdf03dIFiejKR6RZXif5OPRsf8sPwHLQeG9
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Minimization+of+the+maximum+peak-to-peak+gain%3A+the+general+multiblock+problem&rft.jtitle=IEEE+transactions+on+automatic+control&rft.au=Diaz-Bobillo%2C+I.J.&rft.au=Dahleh%2C+M.A.&rft.date=1993-10-01&rft.issn=0018-9286&rft.volume=38&rft.issue=10&rft.spage=1459&rft.epage=1482&rft_id=info:doi/10.1109%2F9.241561&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_9_241561
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9286&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9286&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9286&client=summon